A Robust Three-Dimensional Iterative Solver for the Time-Harmonic Wave Equation

A robust three-dimensional iterative solver for the frequency-domain constant-density acoustic wave equation have been implemented. The linear system arising from the discretisation of the wave equation is solved with a preconditioned conjugate gradient method for non-definite matrices (bicgstab). The preconditioner system is based on a heavily damped wave equation and its inverse is built with one multigrid cycle. The multigrid method fails on the undamped wave equation. 2D and 3D numerical results show that the number of bicgstab iterations is linearly dependent on the frequency.